420 Mr. F. J. W. Whipple on Diffraction of Plane Waves 



related solely to the total charge). Practically, for any 



7? -+- T 

 appreciable cavity, -^ — |r== 1 *, so that (10) becomes for 



any hollow sphere, 



P=-{* L +* L ) (10a) 



The ratio o£ the densities at the inner and outer surfaces 

 is, with L as unit length, 



£_, = R* 2e~^ 2R 2 jR 1 



p 2 R x ' e - B > + e B *- 2 ^ e +A -te~ A ' 



where A = R 2 ~R 1 is the thickness of the spherical shell. 

 If A contains many units (L), we have simply 



%-*%'-*> (10 6) 



P2 J^l 



and if the shell is comparatively thin (A/i? 2 small), the ratio 

 becomes 2e~ A . 



Some further points of the subject of the present paper, 

 and especially those concerning a possible electrostatic 

 estimate of n in connexion with the rigorous non-linearity 

 of the integral equation (non-superponibility) may be reserved 

 for a later opportunity. 



4 Anson Road, N.W. 2. 

 October 8, 1918. 



XL VI. Diffraction of Plane Waves by a Screen bounded by a 

 Straight Edge, By F. J. W. Whipple!. 



IN an article by Mr. R. Hargreaves in a recent number of 

 this Magazine J the diffraction of plane waves by a half- 

 plane is discussed. Mr. Hargreaves is concerned primarily 

 with the case of wave motion according to the simple har- 

 monic law. His method can be adapted, however, to the 

 problem of the diffraction of waves of arbitrary type. The 

 solution of this problem does not appear to have been derived 

 hitherto in terms of such simple analysis §. 



* Only for a full sphere this coefficient becomes — 1, as before. 

 t Communicated by the Author. 

 t Phil. Mag. ser. 6, vol. xxxvi. p. 191. 



§ Cf Lamb, Proc. London Math. Soc. ser. 2, vol. viii. p. 422, and 

 Whipple, idem, vol. xvi. p. 106. 



